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                Freda’s Walk                 </h1>
                <p>时间限制：1s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：128MB</p>			</div>
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                                <h3>题目描述</h3><p><p><span style="font-size: medium">雨后的Poetic Island空气格外清新，于是Freda和Rainbow出来散步。&nbsp;Poetic Island的交通可以看作一张n个点、m&nbsp;边的有向无环图。由于刚下过雨，每条边都有一个积水深度，而恰好Freda&nbsp;和Rainbow都喜欢踩水玩儿，于是Ta们从某个点出发，选择走向哪条边的概率与该边的积水深度是成正比的。即：如果Freda和Rainbow现在在点u，点u&nbsp;出发的所有边的积水深度之和为s，从u到v的边积水深度为w，那么Ta们选择走向v的概率就是&nbsp;w/s。&nbsp; <br />
Ta们会一直走下去，直到到达一个没有出边的点，那么散步的路程长度就是走过的边的数量。更特殊的是，Freda和Rainbow在出发之前还可以选择一条边，在散步过程中无视这条边的存在（当然也可以不选择）。请你帮忙计算一下，Ta&nbsp;们从0号点出发，散步的路程长度的期望值最大是多少？&nbsp;&nbsp;<br />
&nbsp;<br />
&nbsp;<br />
</span></p></p><hr/><h3>输入格式</h3><p><p><font size="4">第一行两个正整数&nbsp;n、m。 <br />
接下来m行每行三个整数u、v、w，表示从u到v有一条无向边，积水深度为w。&nbsp;<br />
&nbsp;<br />
&nbsp;<br />
</font></p></p><hr/><h3>输出格式</h3><p><p><br />
<font size="4">输出Freda和Rainbow散步的路程长度的最大期望值，四舍五入保留六位小数。</font></p></p><hr/><h3>样例输入</h3><pre>4 5 
0 1 2 
0 2 1 
0 3 3 
1 3 1 
2 3 4 </pre><hr/><h3>样例输出</h3><pre>2.000000 </pre><hr/><h3>提示</h3><p><p>对于&nbsp; 100% 的数据，2&lt;=n&lt;=10000，1&lt;=m&lt;=100000，0&lt;=u,v&lt;n，1&lt;=w&lt;=1000。</p></p><hr/><h3>题目来源</h3><p>Adera 2 杯省选模拟赛</p>
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